# The semi-classical limit of large fermionic systems

1 Department of Mathematical Aarhus 2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision 3 Department of Mathematics

Abstract : We study a system of $N$ fermions in the regime where the intensity of the interaction scales as $1-N$ and with an effective semi-classical parameter $\hbar=N^{-1-d}$ where $d$ is the space dimension. For a large class of interaction potentials and of external electromagnetic fields, we prove the convergence to the Thomas-Fermi minimizers in the limit $N\to\infty$. The limit is expressed using many-particle coherent states and Wigner functions. The method of proof is based on a fermionic de Finetti-Hewitt-Savage theorem in phase space and on a careful analysis of the possible lack of compactness at infinity.

Author: Søren Fournais - Mathieu Lewin - Jan Philip Solovej -

Source: https://hal.archives-ouvertes.fr/